WASHINGTON (Reuters) - If Washington doesn't reach a deal soon to keep paying its bills, an economic crisis could start unfolding so quietly on Thursday it will give little hint of its potential to throw millions of Americans out of work.

Many people would not notice right away if the government hits a $16.7 trillion (10.44 trillion pounds) cap on its debt, which could come on Thursday.

Checks would likely go out on time that day for everyone from bondholders to workers who are owed unemployment benefits, according to analysts in government and the private sector.

"The 17th will come, the lights will still be on and everything will look normal for 99 percent of Americans," said Steve Bell, a budget expert at the Bipartisan Policy Centre in Washington.

But that day will also mark America's passage into a period of heightened risk that its financial sector could freeze up in a panic, dealing a potentially severe blow to the nation's businesses and households.

That's because, after then, the government by law will no longer be able to add to the national debt, and will have to rely on incoming revenue and about $30 billion in cash to pay the nation's many obligations.

Unless Congress raised the nation's debt ceiling, the money would be gone within days.

Leaders in the U.S. Senate said on Monday they were close to a deal to raise the debt ceiling and reopen the government but were not there yet.

The Congressional Budget Office estimates Washington would start missing payments between October 22 and the end of the month. America could miss a $12 billion payment due to its Social Security pension program on October 23.

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Around this time, the economy would start sinking like a stone.

To keep from adding to the national debt, the government would slash spending by about a third from one day to the next. Doctors owed money by the government for treating the poor could go unpaid on October 30. By November 1, soldiers could stop getting pay checks on time, and spending would fall across the country.

"Hitting the debt ceiling even briefly could cause the next recession," said Joel Prakken, an economist at forecasting firm Macroeconomic Advisers.

Goldman Sachs estimates the spending cuts could suck the equivalent of about 4 percent of national output out of the economy.

Things would go downhill even more quickly if the government missed debt payments due on October 24 or on October 31.

At that point, there would be a greater risk of a financial crisis because the value of U.S. government debt could be called into question. U.S. debt is used as collateral for trillions of dollars in financial deals, and even Wall Street titans are unsure how scarce credit could become if dealers decide it's no longer worth holding.

"It would ripple through the global economy in a way that you couldn't possibly understand," JPMorgan Chase & Co <JPM.N> Chief Executive Jamie Dimon told a finance conference on Saturday.

Macroeconomic Advisers estimated the spending cuts and a severe credit crunch could cost more than 3 million jobs in America over the next year or so and push the jobless rate to nearly 9 percent.

Already, there are signs of growing fears in financial markets.

In recent days, major money market mutual funds - including Fidelity, JPMorgan and Pimco - have started shunning U.S. debt that comes due between October 17 and the middle of November.

Many analysts think the United States would at least try to keep making bond payments in an effort to keep investors from panicking.

The Obama administration has tried to downplay this possible strategy, saying the government's payment systems weren't designed to decide who gets paid and who doesn't.